How to Make It
Pulse granulated sugar, pink peppercorns, and salt in a food processor until peppercorns are lightly crushed, about 3 times. Add flour, and pulse to combine. Add 1/2 cup butter, and pulse just until flour clumps together when you squeeze it, about 4 times. Add egg yolk and 2 tablespoons half-and-half; process just until dough begins to pull away from sides of bowl and come together, about 10 seconds; adding up to 1 additional tablespoon half-and-half if needed.
Press dough into a disk or rectangle (depending on shape of baking dish); wrap in plastic wrap, and refrigerate 30 minutes or up to 3 days.
Preheat a gas grill to medium. Turn off burners in center, leaving burners lit on either side. Adjust heat as needed to maintain an internal temperature of 375°F to 400°F.
Toss together apples, sugars, lemon juice, cinnamon, vanilla, and salt in a large bowl. Unwrap dough, and transfer to a lightly floured work surface. Roll into a 1/4-inch-thick rustic circle or oval (depending on your skillet or baking dish). Roll dough onto rolling pin, and drape dough over a 12-inch cast-iron skillet or oval Dutch oven, gently pressing dough into bottom and letting excess dough drape over sides. Arrange apple mixture in an even layer on dough, leaving a 1-inch border. Gently fold edges of dough over filling, using your fingers to overlap dough and create a rustic pleated crust. Dot apples with butter.
In a small bowl, use a fork to lightly beat egg and half-and-half until blended. Brush top of dough with egg wash; sprinkle turbinado sugar evenly over dough. Place galette on center (unlit section) of grill. Grill, covered, adjusting heat as needed to maintain an internal temperature of 375°F to 400°F, until crust is golden brown, apples are tender when pierced with a knife, about 1 hour 30 minutes. Serve warm or at room temperature with vanilla ice cream.